= Attainable European contingent claim
{title2=$X_T=\xi$}
= Attainability of a European contingent claim
{synonym}
A maturity-$T$ claim is attainable if a <predictable> <self-financing strategy> with fixed initial capital has terminal wealth equal to the claim payoff almost surely. In discrete time its wealth is $X_t=x+\sum_{s=1}^tH_s\cdot(P_s-P_{s-1})$. The strategy replicates the claim; attainability is a statement about exact pathwise replication, not only equality of <expectations>.
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